Why is the ninth month called September?
late 12c., bileave, replacing Old English geleafa "belief, faith," from West Germanic *ga-laubon "to hold dear, esteem, trust" (cf. Old Saxon gilobo, Middle Dutch gelove, Old High German giloubo, German Glaube), from *galaub- "dear, esteemed," from intensive prefix *ga- + *leubh- "to care, desire, like, love" (see love (v.)). The prefix was altered on analogy of the verb believe. The distinction of the final consonant from that of believe developed 15c.
"The be-, which is not a natural prefix of nouns, was prefixed on the analogy of the vb. (where it is naturally an intensive) .... [OED]Belief used to mean "trust in God," while faith meant "loyalty to a person based on promise or duty" (a sense preserved in keep one's faith, in good (or bad) faith and in common usage of faithful, faithless, which contain no notion of divinity). But faith, as cognate of Latin fides, took on the religious sense beginning in 14c. translations, and belief had by 16c. become limited to "mental acceptance of something as true," from the religious use in the sense of "things held to be true as a matter of religious doctrine" (a sense attested from early 13c.).
a mental attitude of acceptance or assent toward a proposition without the full intellectual knowledge required to guarantee its truth. Believing is either an intellectual judgment or, as the 18th-century Scottish Skeptic David Hume maintained, a special sort of feeling with overtones that differ from those of disbelief. Beliefs have been distinguished according to their degree of certainty: a surmise or suspicion, an opinion, or a conviction. Belief becomes knowledge only when the truth of a proposition becomes evident to the believer. Belief in someone or something is basically different from belief that a proposition is true